Search results for "moments"
showing 10 items of 151 documents
Random Tensor Theory: Extending Random Matrix Theory to Mixtures of Random Product States
2012
We consider a problem in random matrix theory that is inspired by quantum information theory: determining the largest eigenvalue of a sum of p random product states in $${(\mathbb {C}^d)^{\otimes k}}$$ , where k and p/d k are fixed while d → ∞. When k = 1, the Marcenko-Pastur law determines (up to small corrections) not only the largest eigenvalue ( $${(1+\sqrt{p/d^k})^2}$$ ) but the smallest eigenvalue $${(\min(0,1-\sqrt{p/d^k})^2)}$$ and the spectral density in between. We use the method of moments to show that for k > 1 the largest eigenvalue is still approximately $${(1+\sqrt{p/d^k})^2}$$ and the spectral density approaches that of the Marcenko-Pastur law, generalizing the random matrix…
A space-time rainfall generator for highly convective Mediterranean rainstorms
2003
Distributed hydrological models require fine resolution rainfall inputs, enhancing the practical interest of space-time rainfall models, capable of generating through numerical simulation realistic space-time rainfall intensity fields. Among different mathematical approaches, those based on point processes and built upon a convenient analytical description of the raincell as the fundamental unit, have shown to be particularly suitable and well adapted when extreme rainfall events of convective nature are considered. Starting from previous formulations, some analytical refinements have been considered, allowing practical generation of space-time rainfall intensity fields for that type of rai…
Fast Earth Mover's Distance Computation for Catadioptric Image Sequences
2016
International audience; Earth mover's distance is one of the most effective metric for comparing histograms in various image retrieval applications. The main drawback is its computational complexity which hinders its usage in various comparison tasks. We propose fast earth mover's distance computation by providing better initialization to the transportation simplex algorithm. The new approach enables faster EMD computation in Visual Memory (VM) compared to the state of the art methods. The new proposed strategy computes earth mover distance without compromising its accuracy.
Asymptotic potentials and rate constants in the adiabatic capture centrifugal sudden approximation for X + OH(X-2 Pi) -> OX + H(S-2) reactions where …
2012
International audience; New long-range multipolar coefficients for the X + OH(X-2 Pi) interactions, where X = O(P-3), S(P-3) and N(S-4), are given here. They have been evaluated on the basis or monomer properties of the atoms and OH such as the dipole and quadrupole moments, and the static and dynamic polarizabilities. Each matrix element of the 18 x 18 (8 x 8 for N + OH) quasi-degenerate asymptotic potentials has been built up by means of the perturbation theory up to second order including or not the fine-structure of O, S and OH. The adiabatic potentials, obtained after diagonalization of the full matrix, show many crossings and complex behaviors near the asymptotes. Using the entrance c…
A Teaching proposal for the study of eigenvectors and eigenvalues
2017
[EN] In this work, we present a teaching proposal which emphasizes on visualization and physical applications in the study of eigenvectors and eigenvalues. These concepts are introduced using the notion of the moment of inertia of a rigid body and the GeoGebra software. The proposal was motivated after observing students¿ difficulties when treating eigenvectors and eigenvalues from a geometric point of view. It was designed following a particular sequence of activities with the schema: exploration, introduction of concepts, structuring of knowledge and application, and considering the three worlds of mathematical thinking provided by Tall: embodied, symbolic and formal.
Electromagnetic Sensitivity Analysis and Shape Optimization Using Method of Moments and Automatic Differentiation
2009
Sensitivity analysis is an important part of gradient-based optimization of electromagnetic devices. We demonstrate how sensitivity analysis can be incorporated into an existing in-house method of moments solver with a relatively small amount of labor by using a technique called automatic differentiation (AD). This approach enables us to obtain (geometrical) sensitivities of the discrete solution with accuracy up to numerical precision. We compare the assembly time and memory usage of the modified and original solvers. Moreover, we optimize the shape of a dipole antenna and the dimensions of a Yagi-Uda array using the presented AD technique, traditional response level finite difference sens…
New horizons for fundamental physics with LISA
2022
K. G. Arun et al.
Full configuration interaction calculation of singlet excited states of Be3
2004
The full configuration interaction (FCI) study of the singlets vertical spectrum of the neutral beryllium trimer has been performed using atomic natural orbitals [3s2p1d] basis set. The FCI triangular equilibrium structure of the ground state has been used to calculate the FCI vertical excitation energies up to 4.8 eV. The FCI vertical ionization potential for the same geometry and basis set amounts to 7.6292 eV. The FCI dipole and quadrupole transition moments from the ground state are reported as well. The FCI electric quadrupole moment of the X (3)A(1) (') ground state has been also calculated with the same basis set (Theta(zz)=-2.6461 a.u., Theta(xx)=Theta(yy)=-1/2Theta(zz)). Twelve of …
A computational study of some electric and magnetic properties of gaseous BF3 and BCl3
2005
We present the results of an extended computational study of the electric and magnetic properties connected to Cotton-Mouton birefringences, on the trifluoro- and trichloroborides in the gas phase. The electric dipole polarizabilities, magnetizabilities, quadrupole moments, and higher-order hypersusceptibilities—expressed as quadratic and cubic frequency-dependent response functions—are computed within Hartree-Fock, density-functional, and coupled-cluster response theories employing singly and doubly augmented correlation-consistent basis sets and London orbitals in the magnetic property calculations. The results, which illustrate the capability of time-dependent density-functional theory f…
Evidence of a sudden increase in the nuclear size of proton-rich silver-96
2021
Understanding the evolution of the nuclear charge radius is one of the long-standing challenges for nuclear theory. Recently, density functional theory calculations utilizing Fayans functionals have successfully reproduced the charge radii of a variety of exotic isotopes. However, difficulties in the isotope production have hindered testing these models in the immediate region of the nuclear chart below the heaviest self-conjugate doubly-magic nucleus 100Sn, where the near-equal number of protons (Z) and neutrons (N) lead to enhanced neutron-proton pairing. Here, we present an optical excursion into this region by crossing the N = 50 magic neutron number in the silver isotopic chain with th…